On Pareto Local Optimal Solutions Networks

  • Arnaud Liefooghe
  • Bilel Derbel
  • Sébastien Verel
  • Manuel López-Ibáñez
  • Hernán Aguirre
  • Kiyoshi Tanaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11102)


Pareto local optimal solutions (PLOS) are believed to highly influence the dynamics and the performance of multi-objective optimization algorithms, especially those based on local search and Pareto dominance. A number of studies so far have investigated their impact on the difficulty of searching the landscape underlying a problem instance. However, the community still lacks knowledge on the structure of PLOS and the way it impacts the effectiveness of multi-objective algorithms. Inspired by the work on local optima networks in single-objective optimization, we introduce a PLOS network (PLOS-net) model as a step toward the fundamental understanding of multi-objective landscapes and search algorithms. Using a comprehensive set of \({\rho }mnk\)-landscapes, PLOS-nets are constructed by full enumeration, and selected network features are further extracted and analyzed with respect to instance characteristics. A correlation and regression analysis is then conducted to capture the importance of the PLOS-net features on the runtime and effectiveness of two prototypical Pareto-based heuristics. In particular, we are able to provide empirical evidence for the relevance of the PLOS-net model to explain algorithm performance. For instance, the degree of connectedness in the PLOS-net is shown to play an even more important role than the number of PLOS in the landscape.



The authors are thankful to Joshua Knowles and Tea Tus̃ar for fruitful discussions relating to this paper. This research was partially conducted in the scope of the MOD\(\bar{\text {O}}\) International Associated Laboratory, and was partially supported by the French National Research Agency (ANR-16-CE23-0013-01).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Arnaud Liefooghe
    • 1
    • 2
  • Bilel Derbel
    • 1
    • 2
  • Sébastien Verel
    • 3
  • Manuel López-Ibáñez
    • 4
  • Hernán Aguirre
    • 5
  • Kiyoshi Tanaka
    • 5
  1. 1.Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStALLilleFrance
  2. 2.Inria Lille – Nord EuropeVilleneuve d’AscqFrance
  3. 3.Univ. Littoral Côte d’Opale, LISICCalaisFrance
  4. 4.Alliance Manchester Business School, University of ManchesterManchesterUK
  5. 5.Faculty of EngineeringShinshu UniversityNaganoJapan

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